\subsubsection{Amplification and Filtering}
As explained before, the antenna basically consists of an inductor, a capacitor and a resistor. When the rest of the circuit would be applied to the antenna, the total inductance, capacitance and resistance would change, and the antenna will no longer behave as expected. Because of this, it is necessary to make an input buffer.
The design of the input buffer can be seen in \cref{fig:inputbuffer}. The buffer is a simple voltage follower with a high input impedance of $51k\Omega$~. The capacitors are necessary to allow only the AC signal to propagate. Also note that the capacitor $C_B1$ and the resistor $R_E1$ work like a high pass filter.

\begin{figure}[ht!]
\centering
\includegraphics{Assets/InputBuffer.png}
\caption{Input buffer used to connect the antenna to the rest of the circuit}
\label{fig:inputbuffer}
\end{figure}

After the input buffer, the signal should be filtered to minimize the influence of disturbances. Because it is desired to filter out both low frequency and high frequency disturbances, a band pass filter is necessary.
For the $3\mu{}s$ pulses send by the reader the minimum bandwidth should be 333 kHz. The calculation for this can be found in appendix \cref{appendix:bandwidth}.This bandwidth should be centered around the carrier frequency of 13.56 MHz. It is however difficult to create such a steep filter at this frequency, so the bandwidth will be larger.

In this project, there has to be dealt with small signals, so it is important to keep the noise as low as possible. It is most important to keep the noise before the amplification as low as possible; after the amplification, the signal will be larger, so the noise will be relatively small.
Since the filter will be placed before the amplifier, it is not possible to design an active filter with OpAmps, because the OpAmps will cause too much noise.
A solution to this problem is designing a band pass filter built from passive components. Because it is not possible to buffer, all components influence each other. This means that simply placing a low pass and a band pass filter with the right frequency after each other will not result in a band pass filter with the desired pass band. Theory on how a passive band pass filter should be designed can be found in \cite{0750675470}. With this information, it was possible to design the 6th order Butterworth filter. In simulation, this filter worked exactly like expected. However, when the filter was built, the variance of the components and paracitics had so much influence on the pass band, that even when the bandwidth was increased to $5MHz$~, it was not possible to get the pass band at the right frequency.

A solution to this problem was to designing a filter with several transistor stages; first a stage with a transistor amplifier a low pass filter at the collector. After that, a similar stage, but with a high pass filter at the collector. The last stage will be a buffer between the filter and the rest of the circuit.
Because the filter already amplifies, it is not necessary to amplify the signal more. When the filter was built and tested, it was visible that the high pass filter had very little effect on the signal. Almost all the disturbances were caused by the higher harmonics of the $13.56 MHz$ carrier wave. Also, the buffer stage of the filter has a capacitor and a resistor which work like a first order high pass filter. Because of this, it was chosen to leave out the separate high pass stage. The final design of the filter/amplifier can be seen in \cref{fig:filteramplifier}.

\begin{figure}[ht!]
\centering
\includegraphics{Assets/AmplifierAndFilter.png}
\caption{Measurement of the frequency response of the input filter}
\label{fig:filteramplifier}
\end{figure}

The response of the filter was simulation and the results can be found in \cref{fig:filtersimulation}. 

\begin{figure}[ht!]
\centering
\includegraphics{Assets/filtersimulation.png}
\caption{Measurement of the frequency response of the input filter}
\label{fig:filtersimulation}
\end{figure}

It is visible that the filter has a flat response, and has a gain of $26dB$ at $13.56 Mhz$~. After the filter was built, there were measurements done around the frequency we are interested in; $13.56 Mhz$~. These results are shown in \cref{fig:filtermeasurement}.

\begin{figure}[ht!]
\centering
\includegraphics{Assets/spectrumfilter.png}
\caption{Measurement of the frequency response of the input filter}
\label{fig:filtermeasurement}
\end{figure}
